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THE UNIVERSITY OF CHICAGO
A MEASUREMENT OF D* PRODUCTION IN JETS FROM
PP COLLISIONS AT IS = 1.8 TEV
A DISSERTATION SUBMITTED TO
THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES
IN CANDIDACY FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
DEPARTMENT OF PHYSICS
BY
GEORGE REDLINGER
CHICAGO, ILLINOIS
DECEMBER, 1989
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ACKNOWLEDGEMENTS
This experiment was made possible by the diligent work of many
individuals, including the members of the CDF Collaboration, the
technical staffs of the collaborating institutions, and the Fermilab
accelerator division.
I am particularly grateful to my advisor, Henry Frisch, for
supervising my education over the many years. I thank him for letting
me formulate my own analysis, and at the same time keeping an eye on
my progress so as to keep me from straying too far from the optimal
path. I also appreciate his very careful reading of the thesis and his
many helpful suggestions to improve the presentation.
I am also deeply indebted to Brad Hubbard who wrote much of
the efficiency code and whose work led to a dramatic improvement in
the performance of the tracking software. Brad also contributed
enormously to my understanding of the effects of jet energy resolution
on the analysis of jet fragmentation. I have benefitted greatly from
his careful work.
This analysis relied very heavily on the tracking code for
which I would like to acknowledge the work of Peter Berge, Richard
Kadel, Adam Para and Jay Hauser (among many others). I also thank Jay
and Richard for their helpful comments on this analysis. I would also
like to thank Jay for introducing me to the BJD histogram package
which helped me enormously.
I thank Keith Ellis for his help with the QCD calculations,
and I appreciate his patience explaining them to me.
I would like to acknowledge the work of the CDF Jet Group, led
by John Huth, to understand the jet energy scale and resolution; I
have benefitted most directly from the work of Steve Kuhlmann, Steve
Behrends, and Rick St. Denis, to name a few. In addition, I appreciate
the various helpful comments I received from the jet group over the
course of this analysis. I would also like to thank Y.D. Tsai for many
useful discussions about jet physics.
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I
I thank the members of the CDF group here at the University of
Chicago for the pleasure of working with them. I would like to
acknowledge the work of Myron Campbell who developed many of the
computing resources on which I relied quite heavily. I also thank
Myron for teaching me many things about electronics and computing.
thank Dan Amidei and Mel Shochet for the many enjoyable hours we spent
testing the trigger electronics; in this context I also benefitted
greatly from working with Harold Sanders and Joe Ting. I thank Tony
Liss for his guidance in my very early days as a clueless new graduate
student. I have enjoyed many hours of work and conversation with Carla
Pilcher, Aaron Roodman and Paul Derwent. I would also like to thank
Rick Snider for various discussions about physics and for teaching me
many things about tracking.
I am very grateful to Sunil Somalwar for his encouragement
throughout the course of this analysis. I also thank him for all the
enjoyable discussions about optimal filtering and a wide range of
topics both in and out of physics. I would also like to thank Rene Gng
for reading the thesis and for many helpful comments.
Finally I would like to thank the High Energy Physics
department at the U. of C. for providing a stimulating environment in
which to work and to learn.
This thesis is dedicated to my parents.
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i i
LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . vi
LIST OF ILLUSTRATIONS.................... . . . . . . . . . . . . . . . . . . . . . . . .. vii
ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xvi
Chapter
1. INTRODUCTION ............................................. . 1
1.1 Heavy Quark Multiplicity in Jets
1.2 B Physics
1.3 Outline of the Thesis
2. THE CDF DETECTOR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Overview
2.2 Vertex Time-Projection Chamber
2.3 Central Tracking Chamber
2.4 Calorimeters
2.5 Trigger
3. DATA COLLECTION, EVENT SELECTION AND RECONSTRUCTION ....... 29
3.1 Data Collection
3.2 Event Reconstruction
3.2.1 Data ftcleanupft
3.2.2 Jet Reconstruction
3.2.3 Event Vertex Determination
3.2.4 CTC Track Reconstruction
3.2.5 Vertex-Constrained Track Fitting
3.2.5.1 The Beam Position
3.3 Event Selection
3.4 Jet Data Quality
4. SIGNAL EXTRACTION.. . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.1 Method
4.2 The Cuts
4.3 Signal/Background Estimation
4.4 Z Distribution
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5. RECONSTRUCTION EFFICIENCY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84
5.1 Method 5.2 Ptocedure 5.3 D Efficiency
5.3.1 The Average Efficiency for z > 0.1
6. TRACKING RESOLUTION ISSUES ................................ 116
6.1 Method for Estimating the Resolution 6.2 Track Parameter Resolution 6.3 Where Does the Mass Resolution Come From? 6.4 The Efficiency of the Mass Cuts 6.5 Summary
7 . JET ENERGY ISSUES..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 138
7.1 Overview of the Problem 7.2 Correcting the Observed D* Signal 7.3 Results of the Monte Carlo
8. DISCUSSION OF RESULTS..... . . .. .. .. .. . . .. . . .. .. . . . . . . . . . . .. 149
*8.1 The Number of D s per Jet 8.2 Z Distribution 8.3 Possibilities with the 1988-1989 Run 8.4 Conclusion
Appendix
A. THE 1987 CDF COLLABORATION............................. ... 167
B. SOURCES OF TRACKING INEFFICIENCY .......................... 168
C. DETERMINATION OF THE JET ENERGY SCALE ..................... 197
D. DETERMINATION OF THE JET ENERGY RESOLUTION ................ 205
E. MONTE CARLO TO STUDY JET ENERGY ISSUES .................... 211
F. A GLIMPSE AT CORRELATED ELECTRON-D* PRODUCTION ............ 214 REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 219
v
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LIST OF TABLES
1. A summary of the sample of events and jets used in this
analysis, separated by trigger threshold ....................... 48
2. The effect of the cuts applied to extract the D* signal ........ 71
3. The D* efficiency in jets as a function of the
fragmentation variable z, the track multiplicity in the
jet, and the mass difference resolution for z
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LIST OF ILLUSTRATIONS
1. The number of charm quarks per gluon jet as a function of
the Q2 of the gluon................... . . . . . . . . . . . . . . . . . . . . . . . . 5
2. One way to visualize the production of heavy quarks in
gluon jets.................................................... 6
3. The original UA1 evidence for D* production in jets........... 9
4. A cut-away view through the forward half of the eDF
detector. . . . . . . . . . . . . . . . . . . . . . . • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5. Material traversed versus polar angle ......................... 19
6. An end view of the eTC showing the location of the slots
in the aluminum endplates..................................... 22
7. Hadron calorimeter towers in one of eight identical ~-;
quadrants (A;=90·, ~>O)....................................... 25
8. A scatterplot of the x and y positions of the beam for
runs selected for the D* analysis ............................. 43
9. Distributions of the number of tracks per event and the
z-position of the event vertex ................................ 45
10. The ~ distribution of jets with Et (uncorrected) greater
than 10 GeV.................................... . . . . . . . . . . . . . .. 46
11. The corrected Et distribution of jets ......................... 50
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12. Distributions showing the quality of the jet data............. 51
13. The number of tracks inside a cone of radius AR=1.0 with
respect to the jet axlS....................................... 54
14. Mass distributions from a simple Monte Carlo for the *+ 0 + - + + - + 0 +decay sequence: D ~ D ~ + K P ~ ~ K ~ ~ ~ .•.......•...... 57
15. Distributions for tracks from the data sample ................. 60
16. Distributions for the quantity 6.............................. 62
17. The shape in It\c~ of the 6 cut................................. 63
18. The distribution of the cosine of the helicity angle .......... 65
19. The helicity angle versus the opening angle between the
K and the ~ in the lab frame for the decay of a 5 GeV/c
DO in the Monte Carlo................ . . . . . . . . . . . . . . . . . . . . . . . . . 66
20. The expected statistical significance of the signal as
a function of the location of the helicity angle cut .......... 68
21. The distribution of the helicity angle for Monte Carlo
D*s which were merged with real jet data and subjected
to the same cuts as applied in the D* search .................. 69
22. The mass difference distribution from the data after all
the cuts...................................................... 72
23. The mass difference distribution for a straight mass cut ...... 73
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24. Further checks of the signal .................................. 74
25. Examples of fits to the mass difference distribution .......... 78
26. The number of entries per event which make it into the
mass difference plot after all the cuts ....................... 81
27. The mass difference distribution after all the cuts,
broken down into z bins, for both right-sign and wrong
sign track combinations....................................... 83
28. The distribution of the time-over-threshold of hits from
Monte Carlo tracks compared to the data....................... 85
29. The number of hits per track, comparing Monte Carlo
tracks to those from the data................................. 87
30. The layer number of the hits on tracks pass1ng track
selection, comparing Monte Carlo tracks to the data........... 88
31. The input distribution of ; of the Monte Carlo tracks
evaluated at the inner radius of superlayer 4 ......•.•..•.•... 89
32. The number of hits on a reconstructed track which match
those of the Monte Carlo track, divided by the number of
hits on the Monte Carlo track................................. 91
33. The efficiency of the kinematic cuts for D*s as a
function of the fragmentation variable z, broken down
into jet E bins.............................................. 95t
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34. The efficiency of the track selection cuts for D*s as a
tfunction of z, broken down into jet E bins ................... 97
35. The same as Figure 34 except for the cosOH cut ................ 99
36. The same as Figure 34 except for the mass cuts ................ 102
37. The efficiency for finding D*s in jets after all the cuts ..... 104
38. The overall efficiency for finding D*s in jets, folding
in the jet E spectrum........................................ 105t
39. The raw dN/dz spectrum for D*s................................ 107
40. The sensitivity of the efficiency to the slope parameter
P in the parametrization of the raw D* dN/dz spectrum ......... 108
41. The overall efficiency for D*s in high multiplicity
events ........................................................ 110
42. A comparison of the track multiplicity in jets
associated with D* production with that in typical jets ....... 111
43. The effect on the efficiency of changing the AM resolution
in the region of z where the Monte Carlo resolution is
suspect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 114
44. A comparison, in bins of track Pt' of the axial
residuals for tracks in jet events with the residuals
for Monte Carlo tracks ........................................ 119
45. The same as Figure 44 except for the stereo residuals ......... 121
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46. An illustration of how the originating point of the
leading-edge drift electrons differs from the center of
the cell as the angle of the track with respect to the
sense wire plane changes...................................... 122
47. The difference between the reconstructed track Pt and
the true Pt for Monte Carlo tracks merged into jets as a
function of the mean Pt in each bin ........................... 123
48. The same as Figure 47 except for A; ........................... 125
49. The difference between the reconstructed cot9 and the
true cot9 along with a Gaussian fit........................... 126
50. The resolution for the nO mass and the n*-no mass
function of the Pt of the n*....................•............. 128
difference obtained from a "toy" Monte Carlo as a
51. The P of the n daughters from the Monte Carlo aftert ° all the cuts except the mass cuts .......................... '" 131
52. The Pt of the slow pion versus the z of the n* for bins
of jetE ........•............................................ 132t
53. The AM distribution from the data in 0.5 MeV/c2 bins ....•..... 133
54. The efficiency of the AM cut as a function of the AM
resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . .. 135
55. The overall efficiency for finding n*s in jets with
z > 0.1 as a function of the AM resolution in the region
of poor agreement between the data and the Monte Carlo ........ 136
xi
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56. Results from the Monte Carlo showing the effect on R of
an energy scale uncertainty................................... 142
57. The z distribution for D*s from the Monte Carlo, showing
tthe effect of the jet E resolution ..............•....... , .... 143
58. Results from the Monte Carlo showing the effect of the
tjet E resolution on R........... . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 145
59. Results from the Monte Carlo showing the combined effect
of the uncertainty in the jet energy scale and the jet
E resolution on R.......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 148t
60. The Peterson function, commonly used to describe heavy
quark fragmentation, shown for two values of the parameter
€ • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 154
61. A comparison of the data and the predictions of QCD for
the number of charged D*s with z > 0.1 per gluon jet as
a function of the momentum-transfer scale, Q2 ................. 157
62. The fraction of jets which are produced with rapidity
iyi < 0.8 at r; =1.8 TeV and which are initiated
by gluons in the final state.................................. 159
63. The lowest-order QCD calculation for the z distribution
of charm quarks produced in gluon jets (solid curve).
Also shown is the expected z distribution for D*s
assuming a charm fragmentation function given by the
Peterson form................................................. 161
xii
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64. The observed z distribution for n*s, corrected for
detection efficiency.......................................... 162
65. The distribution of the time-over-threshold of hits
from Monte Carlo tracks (before tuning) compared to the
data.......................................................... 169
66. The number of hits per track, comparing Monte Carlo
tracks (before tuning) to those from the data................. 170
67. The layer number of the hits on tracks passing track
selection, comparing Monte Carlo tracks (before tuning)
to the data................................................... 172
68. The single-track finding efficiency as a function of track
Pt for tracks with 1,1 < 1.................................... 173
69. The single-track finding efficiency as a function of track
Pt for tracks with 1,1 < 1 in jet events compared with
minimum bias events........................................... 175
70. The efficiency as a function of the number of cuts
applied for various track Pt bins ............................. 176
71. The 'aspect angle' evaluated at the center of each
super layer for various values of track Pt ..................... 178
72. The number of hits per cell for the five axial superlayers
for jets from a run taken with the 45 GeV trigger ............. 179
73. The number of hits per cell in minimum bias events ............ 180
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74. The single-track finding efficiency as a function of track
Pt for the high multiplicity jet sample, shown together
with the efficiency for more typical jets ..................... 181
75. The number of hits per cell for the high multiplicity
jet data, to be compared with Figures 72 and 73 ............... 182
76. The single-track efficiency as a function of I~I .............. 183
77. The efficiency as a function of the number of cuts
applied for various I~ I bins.................................. 185
78. The single-track efficiency as a function of the r-;
separation between a track and its nearest neighbor ........... 187
79. The efficiency as a function of the number of cuts
applied, for various bins of r-; separation ................... 189
80. The distribution of the r-; separation for the Monte
Carlo tracks above 500 MeV/c.................................. 190
81. The hit density around the track versus the r-;
separation to the nearest track ............................... 191
82. The single-track efficiency as a function of the hit
density around the track.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 192
83. The distribution of the hit density around the Monte
Car10 tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 194
84. The efficiency as a function of ; of the Monte Carlo
track evaluated at the inner radius of superlayer 4........... 195
xiv
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85. The response of the central calorimeters to charged
particles, shown as the ratio of the measured calorimeter
energy to the momentum of the particle ........................ 199
86. The systematic uncertainty in the jet energy correction,
broken down by source......................................... 203
87. A schematic diagram illustrating the definitions of the
e and ~ axes used in the measurement of the jet Et
resolution .................................................. " 206
88. The jet Et resolution as a function of JEt .................... 208
89. An examination of the sensitivity of the resolution
measurement to third-jet activity in the event ................ 210
90. The mass difference distribution in events containing
a central electron............................................ 217
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ABSTRACT
The production rate of charged D * mesons in jets has been measured in 1.8 TeV pp collisions at the Fermilab Tevatron Collider with the CDF
detector. In a sample of approximately 32,300 jets with a mean
transverse energy of 47 GeV obtained from a 1987 exposure of 21.1
nb-1 , a signal corresponding to 25.0 ~ 7.5(stat) ~ 2.0(sys) D*~ + • * * .K ~ ~ events 1S seen above background. This corresponds to a ratio
*+ *- . * N(D + D )/N(Jet) = 0.10 * 0.03 * 0.03 for D mesons with fractional momentum z greater than 0.1. The z distribution is soft with approximately 70% of the observed D*s produced with z between 0.1 and 0.2.
xvi
----_..... _----_.
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CHAPTER 1
INTRODUCTION
Strongly interacting matter is made of quarks, which currently
come in five different "flavors" - u,d,s,c, and b - although there are
both theoretical and experimental reasons 1 to believe that a sixth
flavor, t, must exist. The first three quarks in the list are known as
the "light" quarks since their masses are either comparable or less
than the hadronic mass scale of around 300 MeV/c2 . The remaining two
known quarks, c and b, have masses around 1.5 GeV/c2 and 5 GeV/c2
respectively and are placed in the category of "heavyl quarks. The t
("topl) quark is known to have a mass greater than 77 GeV/c2 at a 95%
confidence level. 2 The production of heavy quarks in hadronic
interactions is a subject of considerable theoretical and experimental
interest.
The basis of the theoretical interest is that heavy quark
production rates in hadronic interactions can be calculated by
applying perturbative techniques to Quantum Chromodynamics (QCD), the
theory of the strong interaction. The argument3 is that heavy quark
production involves momentum transfers on the order of the heavy quark
mass and thus occurs on a very short time-scale. This makes the
problem tractable as it allows one to treat the production process in
terms of three temporally well-separated processes: the evolution of
the initial state of quarks and gluons (collectively known as partons)
inside the hadron, the hard collision between the partons which
produces the heavy quark, and the fragmentation of the final-state
partons into color-neutral hadrons.
Recently, radiative corrections to the heavy quark production
cross section have been calculated4 at third-order in the QCD coupling
1
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2
constant, as' The behavior of these higher-order corrections has
confirmed the applicability of a perturbative calculation.
The experimental interest stems from two broad areas. The
first is to test the predictions of QCD for the production rates, and
to this end, there have been several experiments to measure the
production rates for the charmS and bottom6 quarks. It is important to
verify the QCD predictions for these quarks if we are to have any
confidence in the predictions for the production rates for as yet
undiscovered heavy strongly interacting particles (such as the top
quark). These measurements are also important for an understanding of
backgrounds to new or rare processes whose signatures are often
multilepton final states (which can be mimicked by semileptonic decays
of heavy quarks).
The second source of experimental interest is the hope of
utilizing the high production rates in hadronic interactions to make
precise measurements of the lifetimes, branching ratios, and other
properties of heavy quark bound states; CP violation in the b system
is an example of the last category. The rates are large compared to
those achievable in e+e- collisions. For example, the highest rate in
the next few years for b quark production in e+e- collisions is
expected to be at the Cornell Electron Storage Ring (CESR) where a
peak rate of approximately 0.6 bb pairs per second is anticipated;7 by
contrast the Fermilab pp collider, for example, is already producing
on the order of 10 bh pairs per second. 8 Unfortunately, the detection
of these particles in hadronic interactions is tremendously difficult
due to the enormous flux of background particles accompanying the
breakup of the projectiles. Nevertheless, several groups have taken
advantage of the large production rate in hadronic interactions to
produce competitive measurements of BO-n° mixing9 and some of the most 10sensitive measurements of the lifetimes of charmed mesons and of
Do ,,0 •• 11 -u ml.Xl.ng.
This thesis deals with one part of this rich area of heavy
quark physics. It is a report on a measurement of the multiplicity of
charged D* mesons12 in jets produced in pp collisions at a center-of
http:ml.Xl.ng
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3
mass energy (Ii) of 1.8 TeV using the CDF detector at Fermilab. 13
Indirectly this serves as a measurement of the charm quark
multiplicity in jets (averaged over jet type, e.g. gluon initiated
jets, b quark jets and so forth) since the probability that a charm
quark materializes as a D* meson has been measured. 14
1.1 Heavy Quark Multiplicity in Jets
The multiplicity of heavy quarks in gluon jets has been
calculated in perturbative QCD to be1S
Q2
# of quarks _ ~j dJf a K2
# of gluon jets - 3r 2 K2 s()
Note that this expression differs from the one in the literature by a
factor of two since we are expressing the number of quarks per jet
rather than the number of quark pairs. The quantity n g (Q~K2) is the
'gluon multiplicity·, which is the number of (spacelike) gluons with
4-momentum squared k2 (where K2=_k2) in a jet initiated by a gluon of
4-momentum squared q2 (again, where Q2 =_q2). The gluon multiplicity is
given by
In(Q2 /A2QCD) 1a exp J 6/(rb) In(Q2/AgCD) = [ lnCK /AQCD)
2 2
exp 16/ (rb) In(~ /A~CD)
where
http:Fermilab.13
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4
33 - 2Nf
b = 121"
= the number of participating flavors (i.e. 4)Nf
M= the mass of the heavy quark.
is a parameter of the theory and has to be determinedAQCD experimentally. The current world average value10 1S 200 + l~g MeV for four flavors. The number of charm quarks per jet is plotted in Figure
1 for two extreme values of the charm quark mass and AQCD ; note that
the gluon multiplicity factor can change the result by a factor of two
or more once Q2 gets greater than about (30 GeV)2. Taking Q2 to be the
square of the jet energy, the number of charm quarks per jet ranges
from 0.12 to 0.27 for 30 GeV jets. This corresponds approximately to a
range of 0.05 to 0.10 for the number of charged D* mesons per jet
since the probability that a charm quark materializes as a D*+ or D*
is approximately 3/8. (We will describe this in more detail in Chapter
8.)
The process is schematically illustrated in Figure 2 where a
highly virtual gluon radiates quarks and gluons to reduce its Q2, and
the radiated quanta eventually materialize into color-neutral hadrons.
(From here on, we will use the term Q2 to refer generically to minus
the 4-momentum squared.) The calculation can be thought of as
consisting of two pieces. One is the behavior of the multiplicity of
partons in the cascade down to some cutoff in Q2. This process is now
believed to be rather well understood,16 and is quantified by the
gluon multiplicity factor. The second stage is the production of
hadrons beyond the cutoff point. For light hadron production, this is
incalculable in perturbation theory because the QCD coupling becomes
large. 17 The difference with heavy quarks is that the Q2 of the gluon
has to be at least of order M2 where M is the mass of the heavy2 2 q q
quark. If Mq » AQCD ' then the final stage of the cascade can also
-
--
5
O. 4 M=- 1.2 GeV/c2 , A==350 MeV
0.3 L (J) Q
(/) ~ L
O. :2o ::J cr u
I.+o O. 1
0.0
M .... 1.8 GeV/c 2 , A-=120 MeV
...........-_ ............. -.. -_ .. -_ ........
... -- .... ..,--_ .............-.. "'-_ ..-- .. -_ ... -.. -..........-....... -"'-_.. --_....-..-..... -.......... "' .....
.......................-.
3000o 1000 2000
Figure 1. The number of charm quarks per gluon jet as a
function of the Q2 of the gluon. The formulae of Reference 15 have
been used. The two solid lines show the charm quark multiplicity for
two extreme values of the charm quark mass and AQCD ' The two dotted
lines show the corresponding multiplicity when the gluon multiplicity
factor (see text) is neglected.
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6
Figure 2. One way to visualize the production of heavy quarks
in gluOD jets.
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7
be calculated perturbatively via the Altarelli-Parisi splitting
t · 18f unc 10ns.
One of the big questions in heavy quark calculations is how
heavy the quark must be in order for perturbative methods to be valid.
This is particularly significant for the charm quark whose mass is
approximately 1.5 GeV/c2 to be compared with AQCD of about 0.2 GeV/c2 .
Many of the earlier measurements of the charm production total cross
section, for example, were an order of magnitude higher than the
predictions19 and have led to speculation about alternative mechanisms
for charm production. 20 More recent data, however, seem to indicate
reasonable agreement between QCD and the data. s The nice feature of heavy quark pair production in gluon jets is that the non-perturbative
contributions can actually be calculated,16 and in the case of charm,
the leading non-perturbative correction is found to be five orders of
magnitude smaller than the perturbative contribution. 21
Prior to this calculation, the UA1 Collaboration generated
some excitement when their measurement22 of the D* multiplicity in
jets suggested that the charm content in gluon jets was much higher
than predicted by QCD. 23 As with the charm total cross section, it
appeared that non-perturbative effects would have to be invoked to
explain the discrepancy. The measured rate was N(D*+ + D*-)/N(jet) = 0.65 * 0.19(stat) * 0.33(sys) for D*s with fractional momentum z greater than 0.1. The variable z, commonly used in jet fragmentation
studies, is defined as PD .p. t/ 1p . t 12 • This measurement was based on* Je Je 24
a sample of jets with an average transverse energy of 28 GeV. The
systematic uncertainties were large so that the measured value could
be interpreted as being consistent with QCD predictions; nevertheless
the central value was tantalizing. *+The measurement was performed by looking for the decay D ~
o + 0 - + 26D ~ followed by D ~ K ~ as well as the charge conjugate mode. K-~ and K-~-~ mass combinations were formed using the charged particle
tracks in the central detector. No particle identification was used so
that both K and ~ assignments had to be tried for all tracks. A D* signal would show up as a statistically significant enhancement in the
http:contribution.21http:production.20
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8
number of mass combinations with a K-w mass equal to the Do mass and a K-w-w mass equal to the D* mass. Figure 3 shows the UA1 result; the mass difference 6M =M - ~w is shown for track combinations where Kww the K,w mass was close to the DO mass. There appears to be a nice
signal of an estimated 20 events on a background of 8.
In a subsequent UA1 measurement26 the sample of jets was
enlarged but the signal was much weaker (15 events on a background of
12),27 leading to a much lower multiplicity, N(D*+ + D*-)/N(jet) = 0.08 * 0.02 * 0.04, where the central value is now more in line with QCD estimates. The two measurements differ by about 1.5 standard
deviations; it has been suggested that different trigger conditions in
the two measurements could have contributed to the difference.
The CDF detector enjoys better charged tracking resolution
than UA1. This is essential for the measurement of D* production
because the mass resolution provides the main handle on rejecting the
background from random track combinations. Monte Carlo estimates for
the resolution, using the nominal values for the spatial resolution of
the tracking chambers, are: 28
CDF UA1
14 MeV/c2 34 MeV/c2
0.5 MeV/c2 0.8 MeV/c2
Since the signal-to-noise ratio (SNR) is inversely proportional to the
product of the two values for the mass resolution, CDF has an
advantage of close to a factor of four. This can make a big difference
especially when the SNR is less than one.
1.2 B physics
UA1 measurements of b quark production29 have been primarily
extracted from measurements of muon production, utilizing the
semileptonic decays of b quarks, b + cpv. One of the difficulties of
-
--------------
9
... u ...... >•J: 0)
ci ...... ~ '" c
lIJ •>
The figure is taken from Reference 22. The mass difference AM =M -Krr MKr is shown for track combinations with 1.83 < MKr < 1.92 GeV/c
2 • The
peak near the D·_Do mass difference is evidence for the decay chain *+ 0 + 0 - + •D ~ Dr, D ~ K r and the charge conJugate mode.
10
9
0
136 140 144 148 152 156 160 164
6M-MK..-MKIf (HeV/c2]
Figure 3. The original UA1 evidence for D* production in jets.
-~------------
-
10
this measurement is that several other processes contribute to the
muon rate: • and K decays, muons produced by the Drell-Yan . 30 d f hmechan1sm, ecays 0 c arm mesons, and decays of the J/; and T
resonances. The contribution of these processes is typically 40% of the total rate and the subtraction is not straightforward. The
observation of both the charm meson and the lepton from the
semileptonic decay of the b would provide further evidence that b
decays are being observed. In this context, the search for D*s in jets
serves as a training ground for bottom meson identification. Depending
on how well charm can be identified, one can even imagine
distinguishing semileptonic b decays on an event by event basis. s1
1.3 Outline of the Thesis
The remainder of this thesis is organized as follows. Chapter
2 outlines those parts of the CDF detector relevant to this analysis
and points the reader to detailed documentation in the literature.
Chapter 3 discusses the data collection and reconstruction. Chapter 4
then describes how the D* signal was extracted from the data, and
Chapters 5-7 discuss the treatment of systematic corrections for the
effects of D* detection efficiency and detector resolution. The thesis
concludes in Chapter 8 with a presentation of the results of this work
and a discussion of possibilities for related measurements in the
future.
This is followed by a series of appendices containing more
detailed information about items discussed above. Appendix A contains
a list of the collaborators on this experiment. Appendix B discusses
the sources of tracking inefficiency in more detail. Appendix C
discusses the determination of the jet energy scale and the associated
uncertainty. Appendix D describes the measurement of the jet energy
resolution. Appendix E then describes the details of a Monte Carlo
which was used to estimate the effect of the uncertainty in the jet
energy measurement on our analysis. Finally in Appendix F we describe
http:basis.s1
-
11
a quick search that we performed on a more recent (and larger) data
sample for correlated electron-D* production.
-
CHAPTER 2
THE COF OETECTOR
Our description of the Collider Detector at Fermilab (also
known as the COF detector), will be brief since there exists extensive
documentation in the literature. 32 We begin with a brief overview of
the detector followed by more detailed descriptions of those parts of
the detector most relevant to this analysis.
2.1 Overview
The CDF detector was designed to study proton-antiproton
collisions at the Fermilab Tevatron Collider33 which ran at a center
1029of-mass energy (IS) of 1.8 TeV and a "luminosity" as high as cm-2 I sec- for the data taken for this analysis. The luminosity (which at
2the time of this writing had already reached as high as 2*1030 cm
sec-I) is a quantity which is used to measure the performance of a
colliding beam machine and represents the number of particles crossing
a given area per unit time. It can also be written as
interaction rateLuminosity (L) :: ==;";;;';;;';:(J=::""':::";;;';;;';:;'
-where (J is the cross section for a pp interaction. To give the reader some feeling for the numbers, the inelastic cross section for a pp
interaction at IS=1.8 TeV is estimated34 to be around 60 mb (where 1 2mb :: 10-27 cm ) based on extrapolations from measurements at lower
1029 2 1energies. Therefore, at a luminosity of cm- sec- the
accelerator was producing inelastic interactions at a rate of around 6
12
http:literature.32
-
13
kHz. 3S The p and p 'bunches' crossed each other every 7 ps so there was roughly one interaction for every 24 crossings.
Since collisions at this energy had never been observed in any
accelerator, the CDF detector was designed as a general-purpose
detector capable of observing unexpected 'new' physics as well as
providing solid measurements of 'known' physics. To quote from the
literature, the strategy was to 'measure the energy, momentum and,
where possible, the identity of the particles produced at the Tevatron
over as much of the solid angle as practical·. 36 This was achieved
with the now-standard design of surrounding the interaction region
with charged particle tracking in a magnetic field, followed by
finely-segmented electromagnetic and hadronic calorimeters to measure
the energies of individual particles. Drift chambers outside the
calorimeters are sensitive to muons. This is illustrated in Figure 4
which shows a cut-away view of one half of the detector. The detector
is forward-backward symmetric about the interaction point as well as
cylindrically symmetric about the beam axis. Coverage extends down to
within two degrees of the beam line so that essentially all the
particles produced with significant momentum transverse to the beam
axis are intercepted. The measurement of the vector sum of the
transverse momenta of these particles allows inferences to be made
about the production of neutrinos by using the apparent momentum
imbalance in the transverse plane, a powerful technique previously
exploited by the UA1 Collaboration.
The coordinate system we will use has the x-axis coming out of
the page in Figure 4 (away from the center of the accelerator ring),
the y-axis pointing up, and the z-axis pointing to the left (along the
proton direction); the origin is at the center of the detector. Due to
the cylindrical symmetry of the detector, we will often use the
cylindrical coordinates r,; and z. We will also refer to the polar
angle 6 which is measured in the usual way with respect to the z-axis.
In addition to the polar angle 8, a useful variable in this dimension
for pp interactions is the pseudorapidity (~), which is defined as
~--~~-~-----~~~~~-----~-~--~-~-----~-~-~~-----------------
http:practical�.36
-
Figure 4. A cut-away view through the forward half of the CDF
detector. From Reference 36.
-
15
I
i
C
~ ~ I
-
16
" :: -In(tan ~).
This variable is chosen because of its near equivalence to the
Lorentz-boost variable rapidity (y), defined as
E + p - 1 z y =21 n E _ p ,
z
which in turn is useful because in pp collisions, the center-of-mass
system of the partons are boosted along the z direction in the lab
frame. The rapidity and pseudorapidity are equal for particles whose
masses are negligible compared to their momenta transverse to the z
axis. The detector is segmented uniformly in " and ; since the average
particle density is expected to be approximately uniform in these
variables.
This thesis is based on data from the following detector
components: 1) Vertex Time-Projection Chamber (VTPC) , 2) Central
Tracking Chamber (CTC) , and 3) the calorimeters. We now briefly
describe each of these in turn. In addition, we describe the trigger
system which was used to select the events to be recorded on tape.
2.2 Vertex Time-Projection Chamber37
The VTPC was used in this analysis to determine the z position
of the pp interaction point. It 1S located immediately outside the
beam pipe, and provides information on the r-z projection of the
trajectories of charged particles produced at polar angles greater
than 3.5°. Approximately 2.8m long, the VTPC consists of eight
octagonal modules mounted end-to-end along the beam direction. Each
module has a central high-voltage grid dividing it into two drift
regions. These drift regions were kept fairly short (15.25 cm) in
order for the maximum drift time to be less than the time between beam
crossings (designed to be 3.5 ps). The use of many short TPC's is different from the implementation in e + e - experiments where the
-
17
interaction region can be covered with one module38 due to the longer
time between beam crossings. The TPC records the ionization trail left by the passage of a
charged particle by drifting the ionization electrons away from the
center grid, through a cathode grid, and into one of the two
proportional chamber endcaps. Each endcap is divided into octants with
24 sense wires and 24 cathode pads per octant. The arrival times of
ionization electrons at the sense wires give the z-coordinates of the
track and the positions of the sense wires give the radial
coordinates. Adjacent modules are rotated azimuthally relative to one
another by roughly 11° to eliminate inefficiencies near octant
boundaries and to provide ; information from small-angle stereo. At
polar angles between So and 2So, the wires and pads are instrumented
to encode digitally the pulse shapes, thereby giving another handle on
the; coordinate as well as providing dE/dx information.
Considerable effort was put into minimizing the amount of
material in the VTPC so as to minimize the number of secondary
interactions and the amount of multiple Coulomb scattering. This is
shown in Figure S. The tracks used in this thesis were required to be
in the region ~34° < 8 < ~124°; the amount of material traversed by particles before entering the active volume of the CTC is therefore
less than S% of a radiation length.
2.3 Central Tracking Chamber39
The CTC is located immediately outside the VTPC and provides
precise momentum determination for charged particles in the angular
region 40° < 8 < 140·, The momentum is determined by measuring the particle trajectories in a uniform 1.ST magnetic field produced along
the z-direction by a superconducting solenoid surrounding the chamber.
The CTC is a 1.3m radius, 3.2m long cylindrical drift chamber
measuring up to 84 points per track (depending on the polar angle).
The sense wires are grouped into 9 ftsuperlayersn. Five of these
superlayers (known as the naxial n superlayers) each consist of 12
-
Figure 5. Material traversed versus polar angle. The dots
indicate material traversed before entering the active volume of the
VTPC. The crosses indicate the total amount of material crossed by a
particle as it exits the VTPC system. The triangles indicate the
average total material traversed before entering the active volume of
the CTC or FTC (Forward Tracking Chamber). The figure is from
Reference 39.
-
~-
• Beam Pipe )( VTPC with Faraday Cage
Jj, Total =
1) Above + CTC Graphite Tube
and Inner HV Cylinder
15
20 .
(8) 10°)
2) Above + FTC End Plate0:...< ( 8 < 10°)
For.iI>f ""!l
.-
5 .-
o 1 1-- • 1 Ie ,
,.... o:::.e ~
10
"
o 10 20 30 40 50 60 70 80 90
8 (DEGREES)
-
20
sense wires strung parallel to the beam axis that provide information
on the coordinates of the particles in the r-; plane, again by
measuring the drift time of the ionization electrons. These axial
superlayers are interleaved with four "stereo" superlayers each of
which consist of 6 wires tilted by *3· with respect to the beam axis
and which, through their tilt, provide information on the z-coordinate
of the tracks. The superlayers are divided into cells with a maximum
drift distance of ~ 40 mm, corresponding to a drift time of about 800
ns. Each wire 1S instrumented with multi-hit TDC's (Time-to-Digital
Converters, where multiple times can be recorded before the device
needs to be reset).
Figure 6 shows the endplate of the chamber, illustrating how
the drift cells are tilted by with respect to the radial
direction. This was done to reduce dead space and to keep the drift
time drift-distance relationship linear near the ends of the cells
when the chamber is immersed in the 1.ST magnetic field. The tilted
configuration causes the drift trajectories to be approximately
azimuthal when the magnet is on. There are added advantages of having
the cells tilted at a large angle, and these are as follows:
1) The cells overlap in azimuth so that every track above
roughly 700 MeVjc passes close to at least one sense wire in every
superlayer. This is nice for two reasons. First, it allows one to fit
for "t " o of every track, where by "to" we mean the following. The position of the charged particle is obtained by measuring the arrival
time of ionization electrons onto the sense wires and multiplying by
the drift velocity of these electrons. The arrival times have offsets
associated with them due to signal propagation delays and time of
flight of the charged particles. These offsets are known as to's.
Improved knowledge of the to's leads to improved resolution of closely
spaced tracks. The other advantage of having particles crossing the
sense wire planes is that the resulting "prompt" hits can be used in a
hardware processor to trigger on high transverse momentum (Pt) tracks. 40
-
---------------------------------------------------------
Figure 6. An end view of the CTC showing the location of the slots in the aluminum endplates. This figure is from Reference 39.
-
22
I
-+-I
554.00mm 1.0.
2760.00mm 0.0.
-
23
2) The pattern recognition problem of resolving the 'left
right ambiguity' is simplified. 'Left-right" ambiguity refers to the
fact that the drift-time measurement does not tell us on which side of
the sense wire the particle passed. The rotation of the cell causes
the track segment defined by the improper assignment to be rotated by
a large angle (approximately 70°) so that it fails to match up with
any other segments.
3) Single high-pt tracks sample the full range of drift
distances in the cell; this is useful for the in-situ calibration of
the drift velocity.
The chamber was designed to have a spatial resolution of 200
pm in the r-; plane. This translates to a resolution in the z
direction for the stereo wires of 200pm/sin 3° or approximately 4mm.
This is superior to the resolution one can achieve by the technique of
charge division (where one determines the z-coordinate by comparing
the charge collected at each end of the sense wire) and is furthermore
cheaper to implement since only. the drift time (and not the total
charge collected) needs to be recorded. 41 The price one has to pay is
in the track reconstruction software where the matching of z
information with tracks reconstructed in the r-; plane is more
complicated. The double-track resolution was expected to be less than
5mm, corresponding to a drift time difference of approximately 100 ns.
We will see in Chapter 5 that this is borne out by the data where the
typical widths of the sense wire pulses are around 60 ns.
2.4 Calorimeters42
The calorimeters cover almost the entire solid angle (to
within 2° of the beam). They are arranged in a projective "tower"
geometry in which the calorimeter elements are arranged to point back
to the nominal interaction point. The size of the towers is 0.1 units
in ~ by either 15° or 5° in ; depending on the location. The towers in
the central calorimeter (1~I
-
24
SO in azimuth. Figure 7 shows the segmentation. Each tower consists of an electromagnetic (EM) shower counter followed by a hadron
calorimeter. The EM calorimeters use lead sheets interleaved with an
active medium consisting of scintillator in the central region and
proportional chambers with ftcathode pad readout ft43 elsewhere; the
hadronic calorimeters use steel sheets instead of lead. Proportional
chambers were selected outside the central region for the following
reasons: 1) Since the towers are of uniform size in ~, the actual
solid angle coverage decreases considerably as I~I increases. The
introduction of numerous light guides to bring the light out from all
the small pieces of scintillator would introduce significant dead
areas and non-uniformities in the coverage. 2) In the forward regions,
radiation resistance of the detector is of considerable concern. Gas
systems allow the active medium to be replaced with very little effort
compared to replacing scintillator planes. The price one has to pay is
that the proportional chambers are quite sensitive to the air pressure
which can change quite rapidly depending on the weather. Careful
monitoring of the pressure is therefore required.
Each tower of the central EM calorimeter (I~I < 1.1) is viewed by two phototubes, one on each of the; boundaries. These phototubes
integrate the light output from all layers in the calorimeter. To
provide additional depth information and higher spatial resolution, a
proportional chamber with a resolution of about 2mm is embedded at a
depth of about 6 radiation lengths. Each tower consists of about 18
radiation lengths of material; the magnet coil provides approximately
one additional radiation length. In the plug EM calorimeter
(1.1
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25
. 90- 30- 8 10..f EN:)WALL r-- 1-11"-- FORWARD
l-CENTRAL-1 l-- ENOPLUG --1
.3
;lj Olj v.. h 'Z
I~ ~ ~: :;.-:: 1& rz
&1& 'Z.
:;.-::~ ljOlj
~
...." ...." 'Z 'Z
'Z'Z
~~~
'Z.~
157
131
90
105
0.79
-
26
longitudinal shower profile information, but the planes are divided
into five separate regions per quadrant.
In the hadron calorimeters the sharing of the rapidity
coverage between "central", "plug" and "forward" is different from the
EM calorimeters because of the presence of the magnet coil. In the
central detector there are hadronic towers attached to the back of the
EM towers in the region 1~I
-
27
· 4S. b d1eve1 t r1gger 1S ase on a microprocessor farm, enabling event
selection algorithms to be implemented by software. The multi-level
structure of the trigger was motivated by the desire to introduce as
little bias as possible at the lower levels while reducing the rate
sufficiently so that the next level can do a more sophisticated
analysis without incurring significant deadtime. We will restrict our
discussion to the Level 1 trigger since the other levels were not used
to collect the data for this thesis.
For this data-taking run, the Level 1 decision was based on
the following information:
1) Electromagnetic, hadronic and total Et summed over those
calorimeter trigger towers which are above programmable
thresholds.
2) The existence of high-pt tracks in the CTC.
3) The existence of muon candidates in the central and forward
muon chambers.
4) The presence of a beam-beam interaction and/or the presence
of a beam-gas interaction.
The decision was made in the time between beam cross1ngs so that no
deadtime was incurred. As this thesis is based only on the data taken
with the calorimeter and beam-beam triggers, we will restrict our
discussion only to these.
The projective geometry of the calorimeters is preserved in
the trigger but with coarser segmentation: 0.2 units in q and 15· in ;
for all q. Outputs from all phototubes are brought to the counting room and summed into trigger towers. The gas calorimeter signals are
summed into trigger towers at the detector and then brought up to the
counting room. All the signals are then weighted by sin8 of the
corresponding tower to form the transverse energy deposited in the
tower. To get away from electronic noise, the towers are then required
to have Et above a programmable threshold, typically 1 GeV. The
signals from those towers above threshold are then summed together by
detector component46 and digitized. Digital sums are then made of the
EM, hadronic and total E .t
-
28
The presence of an inelastic pp interaction was identified by
looking for hits in the beam-beam counters (BBC) which cover the
angular region 0.32·
-
CHAPTER 3
DATA COLLECTION, EVENT SELECTION AND RECONSTRUCTION
In this chapter we provide some of the details on how the data
were collected, reconstructed, and selected for analysis. This is
followed by a sampling of plots to provide some idea of the general
quality of the data.
3.1 Data Collection
The data were collected at the Fermilab Tevatron during the
'1987 Collider Run' which nominally began in January of 1987 and ended
in mid-May of the same year. As this was an engineering run for both
the accelerator and for the CDF detector, the first few months of the
run were spent preparing both for serious data-taking. The data for
actual physics analysis were accumulated starting around the beginning
of March.
As mentioned in the previous chapter, the performance of a
colliding beam machine is usually measured in terms of the luminosity,
L, which is defined as follows:
L =observed event rate (J
where (J is the cross section for a pp interaction. Integrated over the
course of the entire run, one obtains the "integrated luminosity"
which is a measure of the number of events of a given cross section
which one expects to be contained in the data collected. The
integrated luminosity delivered by the accelerator during the 1987 run -1 -1 47 was 72 nb of which approximately 33 nb was recorded on tape.
29
-
30
Just to be clear on this concept of integrated luminosity, 33 nb-1
means that if there were a process with a cross section of 1 nb 2(=10-33 cm- ), one would have 33 such events in the data sample. The
average data-taking efficiency for the entire run was 46% (33 nb-1 /72
nb-1 ) although by the end of the run, the efficiency had grown as high
as 83%.48 The sources of deadtime are as follows:
1) Approximately 15% of the collision time was lost by the
need to disable data-taking during certain parts of the Main Ring
cycle. The Main Ring continued to operate, even after the proton and
antiproton beams were stored in the Tevatron, in order to produce
antiprotons which were then collected and stored for future use. Stray
particles from the Main Ring, which passed approximately five feet
above the detector, caused large depositions of energy 1n the
detector, making it impossible to measure the energy from the pp
collisions when the Main Ring beam was present in the collision hall.
2) Deadtime from reading out the detector amounted to a few
percent.
3) The remainder of the deadtime was caused by time to start
new runs, load new gas calorimeter gains into the front-end
electronics, and to change tapes. Early in the run, the time to start
new runs could get quite long S1nce the detector was still being
checked out.
An event was accepted onto tape if it passed anyone of the
triggers described below. All the trigger threshold settings depended
on the luminosity and were chosen so that the rate at which data were
written to tape was approximately 1 Hz. The triggers were:
1) A "jet" trigger requiring either
a) A transverse energy (E ) deposition greater thant 20,30,40 or 45 GeV (depending on the luminosity) summed
over the entire detector, excluding the plug and forward
hadron calorimeters, OR
b) Et > 10,15, or 20 GeV (again depending on the luminosity) in the plug and forward EM calorimeters.
-
31
Only towers with Et > 1 GeV were included in the sum. The hadronic part of the plug and forward calorimeters was not
included in the trigger because of problems with noise on
the front-end electronics and because of the so-called
'Texas towers'. These were clumps of energy caused by
knock-on protons traversing the sampling volume of the
calorimeters at very low velocity (pN1 MeV/c), depositing
much more energy than a minimum ionizing particle. Due to
the relatively low sampling fraction in these calorimeters,
the sensitivity to low energy particles in the hadronic
cascade was magn1'f'1ed . 49
2) A 'central electron/muon' trigger requiring either
a) Et > 7.4, 9, 10, or 12 GeV (once again depending on the luminosity) in a single tower of the central EM calorimetry, OR
b) A track segment in the central muon chambers with
transverse momentum (Pt) greater than 5 or 10 GeV/c
together with a track anywhere in the CTC with Pt
greater than 3, 5.5, or 7 GeVjc.
3) A 'forward muon' trigger requ1r1ng a certain pattern of
hits in the forward muon drift chamber system. This trigger
was rate limited to 0.05 Hz, i.e. events satisfying this
trigger were accepted at the rate of only 0.05 Hz, although
the rate at which this trigger requirement was satisfied
was larger than that. The rate was high due to spurious
hits in the chambers from beam fragments interacting in the
'low-pI quadrupole magnets situated around the beam pipe in
the forward region. (See Figure 4.)
4) A 'minimum bias' trigger requiring one hit on each side of
the interaction region in the beam-beam counters within a
15ns window centered on the beam-crossing time. This
trigger was also rate limited to 0.05 Hz.
Triggers 1 through 3 required, in addition, the "minimum bias' trigger
to have been satisfied. Only Trigger 1 was used in this analysis.
-
32
3.2 Event Reconstruction
The first pass through the data for the D* analysis was to go
through all the data tapes, selecting those events which passed the
"jet" trigger described above. Good runs were selected on the basis of
the number of "Main Ring events" per run, the average number of jets
per event, problems with the monitoring of the luminosity, trigger
problems, and high voltage problems. More specifically, the cuts
required good runs to have ~ 1~ of the events to be Main-Ring-induced
and an average number of jets (with Et > 25 GeV) per event greater than 0.02. Approximately 1.5*105 events were selected, corresponding
to about g~ of the events passing the jet trigger.
3.2.1 Data "cleanup"
The events were then subjected to a series of software filters
which either fixed known problems in the calorimetry data or discarded
events which were not worth repairing. We should emphasize that only a
small fraction of the events were affected. We will describe only
those filters which affect the data in the central detector since this
analysis is concerned only with jets in the central region (for which
full tracking coverage exists).
1) First event after a pause in the data-taking
This filter rejected the first event in each run as well as
the first event after a long pause (> 20 sec.) in the datataking. The reason for this was that during long pauses the
voltage levels on the output of the front-end electronics
drifted up to (and were pinned at) the power supply
voltage, equivalent to an unphysical amount of energy
deposited in the calorimeter. Approximately 0.5~ of the
events were rejected in this way.48
-
33
2) Pedestal correction50
The average DC offset on the front-end electronics when no
energy was deposited in the calorimeter is known as a
"pedestal". For each calorimeter tower, the pedestal value
was obtained during calibration runs taken while the beam
was off. For some channels, however, this procedure gave
unsatisfactory pedestal calibrations due to differences in
noise conditions between calibration runs and actual data
taking. The minimum bias data (in which there is relatively
little beam-related activity in the calorimeters) were
therefore used to identify channels with significant shifts
in the pedestal value. Only two of the approximately 2300
channels in the central calorimeters had their pedestal
values corrected. 48
3) "Bot" phototube suppressionS1
The photomultiplier tubes in the central calorimeters
experienced electric discharges at a low rate between the
photocathode and the mu-metal shielding. Since essentially
all the towers in the central calorimeters are viewed by
two phototubes, these discharges were identified by
comparing the signals in the two tubes. Using the pulse
heights in the two tubes, the width of the calorimeter
tower, and the attenuation length of the scintillator, a
shower center relative to the center of the tower was
calculated. The uncertainty 1n the shower position was
calculated using Poisson statistics on the total number of
photoelectrons. A signal was declared to be spurious when
the shower center was more than three sigma outside the
physical boundary of the tower. The energy in the tower was
then set to the energy seen by the other phototube. Again,
this was a small effect (~1~), although unfortunately we
have not been able to find the exact number of events which
had hot phototubes.
http:corrected.48
-
34
4) Main Ring and Cosmic Ray Induced Showers52
We have described earlier how the detector was gated off
during certain parts of the Main Ring cycle to veto events
caused by stray particles from the Main Ring. Some
particles, however, still managed to enter the detector
outside the veto gates. In addition, the calorimeters are
subjected to constant bombardment from cosmic ray muons,
some of which deposit significant amounts of energy via
bremsstrahlung in the calorimeter material. Both of these
types of events were identified by their timing relative to
the beam crossing time using the TDC's (Time-to-Digital
Converters) in the central and endwall hadron calorimeters.
Energy deposited outside a time window ranging from -10 to
+25 ns in the central calorimeters and between -10 and +55
ns in the endwall with respect to the beam-crossing time
was declared to be "out-of-time". Only towers with energy
greater than 1 GeV were used due to the degradation of the
timing accuracy at lower energies. Towers with times equal
to exactly 0 (again with energy greater than 1 GeV) were
also flagged as anomalous. Since the TDC's are very
efficient for energies above 800 MeV, the absence of a TDC
hit indicated that either the channel was dead or that
energy was deposited during the 150 ns interval (occurring
N200 ns before beam crossing) during which the ADC's are
enabled but the TDC's are not. The following criteria were
then used to reject events:
1) > 8 GeV in the out-of-time towers, OR 2) > 8 GeV in the towers with t=O.O.
Less than approximately 0.5% of the events were rejected.
The filter was essentially 100% efficient in rejecting Main
Ring splashes since the extent in time of the splashes was
long enough that there were always enough towers out-of
time. For cosmic ray bremsstrahlung, it has been estimated
that the filter is around 90% efficient. The remainder of
-
35
the cosmic rays either fall within the in-time window or
shower in the EM calorimeter which was not equipped with
TDC's. We will come back to these later.
5) CTC Noise
The CTC occasionally experienced "bursts" of noise in which
noise from a few wires spread through large regions of the
chamber by electronic crosstalk between wires. The noise
was from low-energy electrons (p N 100 keV/c to 1 MeV/c)
from the uranium absorber in the crack detectors which are
located at 15° intervals in ; outside the CTC. These
detectors cover the cracks in the central calorimeter
coverage where the light guides are brought out. The
signals from such electrons are large (approximately 100
times minimum ionizing) because the electrons tend to
spiral around a single wire, causing the amplifiers on the
pulse-shaping electronics to ring. These bursts were
flagged by looking for contiguous sets of drift cells in
which all wires were hit within a narrow time window.
Approximately 1% of the events were rejected in this way.
Since 1987 the uranium has been replaced by tungsten, and
the grounding on the front-end electronics has been
fortified.
3.2.2 Jet Reconstruction
After the calorimeter energies were determined to the best of
our knowledge, jets were reconstructed, where jets are defined
operationally as localized depositions of energy in the calorimeter.
To make contact with theoretical calculations, jets are identified
with the hadronized end-product of a scattered quark or gluon. This
definition is reasonable since most of the physical particles into
which the parton materializes are observed to have a fairly limited
momentum (on the order of 400 MeV/c) transverse to the direction of
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36
the parton. The direction of the original parton is thus fairly well
preserved (at least for jets with E greater than approximately 15t GeV).
The jet-finding program proceeded as follows. Calorimeter
towers with E greater than 1 GeV were selected as starting points, ort 'seeds', for cluster finding. The remalnlng towers with E > 200 MeVt were then considered as candidates for clustering. 'Preclusters' were
formed around each seed tower by looking for an unbroken chain of
adjacent towers with E continuously decreasing as one got furthert from the seed tower. Preclusters with total E greater than 2 GeV weret then used as starting points for further clustering. The centroid of
the precluster was defined by the energy-weighted mean
[ ' ~.Eti 1towers
[ Eti towers
[ ' ;.Eti 1towers [ Eti
towers
All towers above 200 MeV inside a fixed cone in ~-; space with a
radius53 of 1.0 with respect to the precluster centroid were then
added to the precluster to form a cluster. A new centroid was
calculated for this newly formed cluster and again all towers within a
cone around the new centroid were merged into the cluster. For each
precluster , the process was repeated until no more towers were added
to the cluster.
Overlapping clusters were treated as follows. An 'overlap
fraction' was computed as the sum of the E of the common towerst divided by the E of the smaller cluster. Two clusters were combinedt when the overlap fraction was greater than 0.75. This number should be
treated as part of our experimental definition of a jet. In cases
where the overlap fraction was less than 0.75, the clusters were kept
separate and the energy in the overlapping towers was assigned to one
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37
or the other cluster depending on the distance of the tower to the
cluster centroid. Aiter all the overlapping towers were assigned to a
cluster, the centroids were recomputed and the original overlapping
towers were reassigned depending on the distance to the new centroids.
The process was then repeated until no towers needed to be reassigned.
Several different clustering algorithms were tried and their
performance was compared with the fixed-cone algorithm described
above. 54 The main tests were to compare the ability of the algorithms
to resolve closely spaced jets and to see how much energy was
misassigned between two nearby clusters which had not been merged.
This was done with a sample of clean two jet events in which there
were no other jets above 5 GeV. The calorimeter information from pairs
of such events were combined, and the clustering algorithms were run
on the merged event. For the first test, the fraction of time that
separate clusters were merged was examined as a function of the ~-;
separation between clusters. The fixed-cone algorithm was found to
have the sharpest cutoff in ~-; space beyond which two separate
clusters could be rescllved. In the second test, the E of the clusterst in the unmerged events was compared to those in the merged events.
Again the fixed-cone algorithm was found to be the most stable with
the smallest difference. In addition, the fixed-cone algorithm is
thought to lend itself more naturally to theoretical calculations
since it is most closely related to the way in which collinear
singularities are regulated in calculations of gluon bremsstrahlung. 55
Based on these features, the fixed-cone algorithm was crowned the
algorithm of choice for CDF.
Jets were reconstructed over all of the calorimeters. The Et of the jet was computed by taking the sum of the EM and hadronic
energies of the towers in the jet and multiplying by the sine of the
polar angle defined by the jet energy centroid. The UA2 Collaboration
has used a weighted sum of EM and hadronic energies to define the jet
energy.56 Studies with CDF jet data57 seem to indicate, however, that
in the CDF detector a simple sum provides the same jet energy
resolution as a separately weighted sum.
http:energy.56http:above.54
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--
38
3.2.3 Event Vertex Determination
The position of the event vertex along the beam axis was
determined by finding tracks in the r-z projection in octants of the
VTPC, fitting them to straight lines, extrapolating them to the beam
(r=O) and then searching along the beam axis for clusters of points
where the track segments intersected the beam axis. The event vertex
was determined from the position of the cluster with the largest
number of tracks. The precise details of this procedure are described
elsewhere. 58 The vertex distribution is well described by a Gaussian
with a sigma of approximately 35 cm and a mean of +3.6 cm from the
nominal center of the detector. On an event-by-event basis, the vertex
is determined with an accuracy of approximately 1mm where the
uncertainty is dominated by systematics and comes from the lack of
knowledge of the position of the VTPC relative to the rest of the
detector. 59
3.2.4 CTC Track Reconstruction
Before getting into the CTC track reconstruction program, let
us briefly recall some of the features of the chamber. As we mentioned
in Chapter 2, the CTC is a cylindrical drift chamber immersed 1n a
1.ST axial magnetic field. The sense wires are grouped into
superlayers, five of which (ftaxial ft superlayers) are strung parallel
to the z-axis and the remaining four (ftstereo ft superlayers) which are
tilted by *3· with respect to the z-axis. Axial and stereo superlayers
alternate as one goes along the r-direction. The axial layers measure
the rand; coordinates of charged particles, and the stereo layers
measure the z coordinate. Momentum information for charged particles
is obtained by measuring the curvature of the helical trajectory of
the particle in the magnetic field.
The CTC track reconstruction program is divided naturally into
two parts: reconstruction of tracks in the r-; projection using the
axial wires, followed by full 3-dimensional reconstruction combining
http:elsewhere.58
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39
the r-; view with z information from the stereo wires. The r-;
reconstruction begins by looking in the outermost axial superlayer for
a set of hits which is consistent with a line segment crossing the
sense wire plane. Once such a segment is found, the search for other
hits from this potential track is conducted both inward and, when
possible, outward in a circular road passing through the segment and
the z-axis. The search is repeated, using a better starting
approximation of the trajectory on each iteration, until no more
acceptable hits are found. The search for "seed" segments not already
associated with tracks continues inward through all the axial
superlayers.
The z reconstruction uses the track parameters determined in
the r-; reconstruction to look for line segments in each of the stereo
superlayers whose slopes relative to the predicted position of the
track (at z=O) are small. The z position of each segment is determined
from the r-; distance between the segment and the location of the
track at z=O. Once line segments have been selected as candidates for
the track, the segments which best match the track are found by
fitting all combinations of segments (there can be several segments
per stereo superlayer) to a linear function in z and ;. The set of
segments with the smallest X2 is then used to get a first approximation of the polar angle of the track. The search for stereo
hits is then repeated from scratch, this time using the approximate
polar angle to restrict the search region.
A fit to a helix is then performed. The helix is described by
five parameters:
1) Half-curvature, C. This is the inverse of the diameter of the circle traced out by the particle in the r-; plane. It is a signed quantity, where the sign depends on the charge of the particle.
2) Distance of closest approach, D, also known as the impact parameter. This is the shortest distance in the r-; plane between the track and the origin. It is easy to show that this is the distance between the track circle and the origin measured along a line passing through the center of the circle and the origin. The impact parameter is also a signed quantity where the sign depends on the charge of the
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40
particle and whether or not the origin is enclosed by the track circle.
3) Azimuthal angle, ;0' This is the azimuthal angle of the tangent to the track at the point of closest approach.
4) Cote, where e is the polar angle of the track at the point of closest approach.
5) Zo' the z position of the track at the point of closest approach.
3.2.5 Vertex Constrained Track Fitting
Tracks with an impact parameter less than 0.5 cm were refit
with the added constraint that they pass through the event vertex, the
position of which is measured with the VTPC to higher precision than the pointing accuracy of the eTC itself. The method used to constrain
the tracks to the vertex is described in detail in the literature. 5o
We give a brief summary here. The functional dependence of the five ..track parameters (denoted by the vector p) on the position of the
.. ... . event vertex (x) and the track momentum (q) at the vertex 1S wr1tten
as a linear expansion about approximate values of ~ and q (denoted by .. .. xo and Cia) as follows:
.. .. .. ... .. ... p = p +A'(x-x) + B' (q - Cia) [3.1J
0 0
where A and B are the following 5-by-3 matrices
oPi oPi OPi ox oy oz
A =
oPs . . , . 8ps ox oz
B =
oPl 8Pi oPi
a~ a~ 8~
oPs oPs . . . , oqo~ z
http:literature.5o
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41
and where Pi through p denote the five track parameters. Both 5.. .. ....
matrices are evaluated at (xo,~). The vectors x and q are determined
by minimizing a chi-square which is formed between the measured track .. .. parameters Pobs and the track parameters, Pexp' calculated with
equation 3.1, i.e.
where G is the inverse of the 5-by-5 covariance matrix of the measured .. ..
track parameters. The values of x and q determined in this way are
then plugged into equation 3.1 to obtain the vertex constrained track
parameters.
Multiple scattering in the material before the sensitive
volume of the CTC « 5% of a radiation length) was neglected. There was a provision in the fitting routine to take multiple scattering
into account by appropriately incrementing the covariance matrix of
the track parameters, but this was found to have only a small effect
on the results of the vertex constrained fit. 51
3.2.5.1 The Beam Position
We have described earlier how the position of the z-component
of the event vertex was determined from the r-z projections of tracks
in the VTPC. We now describe how the x,y components of the vertex,
namely the beam position, were determined with respect to the CTC. In
the approximation that the radius of curvature of the track is much
larger than the impact parameter (a condition that is met by all
observed tracks), one can show that the dependence of the impact
parameter, D, for primary tracks on ;0 is given by
[3.2J
Writing the beam position as a linear function of z, i.e.
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42
= ax + b zxBeam x ~am=~+\z
the parameters a, b, a, and by were determined by fitting the x x y impact parameter of 3-dimensional tracks versus the z-intercept and ;0 according to the form given by equation 3.2. If the X2 contribution of a track was greater than 10 (where the a on the impact parameter was
set to 500 pm), it was set to 10 so as to keep the fit from getting
pulled by poorly measured or non-primary tracks.
The beam position constants which we used were derived from
the minimum bias data and are as follows:
a x = -550 pm a y = -130 pm b = 2.8 pm/cm by = -1.0 pm/cmx
A systematic error of 60 pm was assigned to both the x and y
coordinates of the beam. As a check of the beam position, we repeated
the analysis for the jet data; the results are summarized in Figure 8
for three values of z. The boxes mark the limits of the beam
coordinates obtained from the minimum bias data. The difference is
probably due to the fact that the minimum bias analysis used an
earlier version of the track reconstruction program. Whatever the
reason, we felt that the difference was not large enough to warrant
refitting all the tracks with run-by-run beam position constants. Our
reasoning was that masses which are reconstructed from two oppositely
charged tracks (e.g. the DO) should not be terribly sensitive to small changes in the beam position because the increase in momentum of one
track is balanced by a decrease in that of the other.
3.3 Event Selection
Starting with approximately 1.5'105 triggers, a first
reduction of the data was achieved by requiring the leading jet, i.e.
-
••
43
:200
~
E 0 ::t
'-../
~
E 0 OJ
..0 '-../
-:200
>
-400
•
• .+
+. •. • +. . .... ... ... ..+ >1
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44
the one with the highest E , to have E greater than a thresholdt t depending on the trigger hardware threshold as follows:
Trigger threshold (GeV) Leading jet threshold (GeV) 20 20 30 25 40 40 45 40
Only jets with an EM fraction, i.e. (EM Et)/(Total E ), greater thant 0.01 were considered in order to cut out cosmic ray showers in the
hadron calorimeter which were in-time with the beam-crossing. This
reduced the sample to approximately 6.5'104 events.
Only a subsample of these events were subjected to further
selection cuts. Because the track reconstruction program requires a
fair amount of CPU time (on the order of 40 sec. per event on the VAX
8600), it was impossible to track all of the selected events, given
the heavy load on the Fermilab computing resources at the time. As a
result only 4.3'104 of the approximately 6.5'104 events selected were
actually tracked. Events were then required to have at least one well
measured track (to reject events in which the eTe was temporarily off)
and a vertex within 60 cm of the center of the detector, reducing the
number of events to 3.8'104 . Figure 9a is a distribution of the number
of tracks per event before the cut was applied on this quantity.
Figure 9b shows the event vertex distribution along with a Gaussian
fit.
Further cuts were applied to select the jets for this
analysis. To ensure that the jets were well-contained within the
central calorimeter, jets were required to have an energy centroid 1n
the range 0.1 < I~I < 0.8. Figure 10 shows the jet ~ distribution on which these cuts were applied. The rapid falloff in the distribution
for 1~1~1.0 is due to the fact that the hadronic part of the
calorimeters in this region was not included in the trigger. There is
also a dip at the center due to the crack in the detector where the
two halves of the central detector meet. Energy lost 1n the
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45
1500
(f) ..... C IV > IV 1000 -0 I... IV ....,500.D E ::J Z ~
-! 0
0 20 40 60 eo
No. of good trocks/event
E 2000 0
....r 1500
..........
(f) ..... C IV 1000>IV
-o I... 500 IV
.D E ::J Z 0
-100 -50 o 50 100
Z position of event vertex (c nn)
Figure 9. Distributions of the number of tracks per event and
the z-position of the event vertex. a) The number of well-measured
tracks per event in the tracked jet data. b) The distribution of the
z-position of the event vertex together with a Gaussian fit.
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46
3000
~
0 2000
""(J) -+-' (])
'--'
4
0 1000 I.... (])
.D
E :::I
Z
0 -"'4 -2 0 2
7J of jet
Figure 10. The ~ distribution of jets with E (uncorrected)t greater than 10 GeV. The jets are from events passing the event selection criteria for this analysis.
-
47
uninstrumented crack caused fewer jets in this region to pass the
trigger requirement.
The jet energies were then corrected for the following
effects: 1) the nonlinear response of the calorimeter to low-energy
charged particles, 2) energy deposited in uninstrumented regions, 3)
energy lost outside the clustering cone, and 4) energy gained from the
"underlying event", i.e. that energy which is not associated with the
hard parton scattering. These corrections are described in more detail
in Appendix C. For typical jets in this analysis, the correction
increased the jet energy by 25%. The corrected Et of the jets was then
required to be greater than 30 GeY. Figures 11a-11d show the corrected
jet E distributions fc)r the four jet trigger thresholds before the 30t GeY cut was applied. The sharp edges in the plots reflect the cut on
the leading jet E applied early in the event selection process. Thet Et distribution for the jets used in the D* search is shown in Figure
11e. Table 1 summarizes the cuts applied to select our sample of
events and jets.
3.4 Jet Data Quality
We conclude this chapter with a small collection of plots to
give a flavor of the quality of the jet data (Figure 12). The tracking
data will be addressed in the next chapter. The azimuthal separation
of the two leading jets in each event is peaked at 180·, indicating
the dominance of two-jet events. The jet ~ distribution shows the
expected azimuthal symmetry, indicating the absence of any "hot"
towers in the calorimeters. The "charged fraction", which we have
defined as the scalar sum of the Pt of well-measured tracks within a
cone of radius 6R=1.0 about the jet axis divided by the corrected jet
E